=1/2(1/2+1/6+1/12+1/20+...+1/90)

=1/2(1-1/2+1/2-1/3+...+1/9-1/10)

=1/2*9/10=9/20

Cô Hoài ơi, cô trả lời tin nhắn em với ạ!

a, (-25) + 276 - (276 - 25)

= (-25) + 276 - 276 + 25

= [ (-25) + 25] - (276 - 276)

= 0 - 0

 = 0

b, 24 x 46 + 24 x 53 + 24 

= 24 x ( 46 + 53 + 1)

= 24 x 100

= 2400

c, 145 + 20 - 45 + 180

= (145 - 45) + (20 + 180)

= 100 + 200

= 300

d; 12 x 36 + 12 x 65 - 12

= 12 x ( 36 + 65  - 1)

= 12 x (100)

= 1200

1. Cho phân số a/b, b>a. C/m :

a) Nếu a/b < 1 thì a+1/b+1 > a/b

b) Nếu a/b > 1 thì a/b > a+1/b+1

2. Tính :

3/4 + 3/12 + 3/24 + 3/40 + 3/60 + 3/84 + 3/112 + 3/144 + 1/180

Toán lớp 6

A = 1/4 x 8 + 1/8 x 12 + 1/12 x 16 + ... + 1/176 x 180

=> 4A = 4/4 x 8 + 4/8 x 12 + 4/12 x 16 + ... + 4/176 x 180

=> 4A = 1/4 - 1/8 + 1/8 - 1/12 + 1/12 - 1/16 + ... 1/176 - 1/180

=> 4A = 1/4 - 1/180

=> 4A = 45/180 - 1/180

=> 4A = 44/180

=> 4A = 11/45

=> A = 11/45 : 4

=> A  = 11/180

Vậy A = 11/180

A = \(\dfrac{1}{4\times8}\) + \(\dfrac{1}{8\times12}\) + \(\dfrac{1}{12\times16}\) +...+ \(\dfrac{1}{176\times180}\)

A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{4}{4\times8}\)+ \(\dfrac{4}{12\times16}\)+...+ \(\dfrac{4}{176\times180}\))

A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{12}\) - \(\dfrac{1}{16}\) +...+ \(\dfrac{1}{176}\) - \(\dfrac{1}{180}\))

A = \(\dfrac{1}{4}\) \(\times\)(\(\dfrac{1}{4}\) - \(\dfrac{1}{180}\))

A = \(\dfrac{1}{4}\) \(\times\)\(\dfrac{11}{45}\)

A = \(\dfrac{11}{180}\)

2A=1/2+1/6+1/12+1/20+1/30+1/42

    =1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

    =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

    =1-1/7

    =6/7

1: \(\Leftrightarrow x=UCLN\left(24;36;150\right)=6\)

2: \(\Leftrightarrow x\in\left\{24;48;72;...\right\}\)

mà 16<=x<=50

nên \(x\in\left\{24;48\right\}\)

3: \(\Leftrightarrow x\inƯ\left(6\right)\)

mà x>-10

nên \(x\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

4: \(\Leftrightarrow x\in BC\left(4;5;8\right)\)

\(\Leftrightarrow x\in\left\{...;-40;0;40;80;120;160;200;...\right\}\)

mà -20<x<180

nên \(x\in\left\{0;40;80;120;160\right\}\)

Cho tg tren la A

A=\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)

\(A=2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{14}\right)\)

\(A=2.\frac{3}{7}\)

\(A=\frac{6}{7}\)

A = 1/4 + 1/12 + 1/24 + 1/40 + 1/60 + 1/84

            = 2 ( 1/2*4 + 1/4*6 + 1/6*8 + 1/8*10 + 1/10*12 + 1/12*14 )

            = 2 ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12 + 1/12 - 1/14 )

            = 2 ( 1/2 - 1/14 )

            = 6/7